Method and Apparatus to Perform Optimal Visually-Weighed Quantization of Time-Varying Visual Sequences in Transform Space

ABSTRACT

Pure transform-based technologies, such as the DCT or wavelets, can leverage a mathematical model based on few or one parameters to generate the expected distribution of the transform components&#39; energy, and generate ideal entropy removal configuration data continuously responsive to changes in video behavior. Construction of successive-refinement streams is supported by this technology, permitting response to changing channel conditions. Lossless compression is also supported by this process. The embodiment described herein uses a video correlation model to develop optimal entropy removal tables and optimal transmission sequence based on a combination of descriptive characteristics of the video source, enabling independent derivation of said optimal entropy removal tables and optimal transmission sequence in both encoder and decoder sides of the compression and playback process.

PARENT CASE TEXT

This application claims benefit of a prior filed U.S. provisionalapplication, Ser. No. 61/818,419, filed May 1, 2013.

REFERENCES

ISO/IEC 15444-1:2000

Information technology—JPEG 2000 image coding system—Part 1: Core codingsystem

US Patent Documents

U.S. Pat. No. 6,239,811 Westwater

Method and apparatus to measure relative visibility of time-varying datain transform space

U.S. Pat. No. 8,422,546

FEDERALLY SPONSORED RESEARCH

Not Applicable.

BACKGROUND

1. Field of Invention

The present invention relates generally to compression of moving videodata, and more particularly to the application of quantization of thethree-dimensional Discrete Cosine Transform (DCT) representation ofmoving video data for the purposes of removing visually redundantinformation.

2. Description of Prior Art

It is well established in the literature of the field of videocompression that video can be well-modeled as a stationary Markov-1process. This statistical model predicts the video behavior quite well,with measured correlations over 0.9 in the pixel and line directions.

It is well-known the Karhunen-Loeve Transform (KLT) perfectlydecorrelates Markov-distributed video. This means the basis of the KLTis an independent set of vectors which encode the pixel values of thevideo sequence.

It is a further result that many discrete transforms well approximatethe KLT for large correlation values. Perhaps the best-known suchfunction is the DCT, although many other functions (DST, WHT, etc.)serve as reasonable approximations to the KLT.

It is for this reason the DCT is used to decorrelate images in the JPEGstandard, after which a uniform quantization factor individually chosenfor each DCT component is applied to said component, removing visualinformation imperceptible to the human eye. FIG. 1 illustrates the useof a Human Visual System quantizer array in JPEG. An individual frame ofdigitized video Error! Reference source not found 010 is transformed viaa two-dimensional DCT Error! Reference source not found 020 and thenquantized Error! Reference source not found 020 to remove imperceptiblevisual data. An entropy removal process Error! Reference source notfound 040 actually compresses the information. The decompression processfollows an equivalent set of steps in reverse, when a data set or datastream containing the compressed data Error! Reference source not found210 is decompressed Error! Reference source not found 110 by reversingsaid entropy removal process, followed by a de-quantization step Error!Reference source not found 120, an inverse DCT step Error! Referencesource not found 130, and a resulting frame Error! Reference source notfound 140 may be displayed or otherwise processed. A key part of theprocess is good choice of quantizers Error! Reference source not found310 that leverage a Human Visual Model to optimally remove redundantinformation. The use of a Human Vision Model in terms of a ContrastSensitivity Function to generate two-dimensional quantizer coefficientsis taught by Hwang, et al, and by Watson U.S. Pat. No. 5,629,780.

FIG. 2 illustrates the use of the DCT in the prior-art MPEG standard. Ablock-based difference after motion estimation 2015 is taken betweenreference frame(s) 2010 and an individual frame to be compressed 2005.Said block-based difference after motion estimation 2015 is transformedusing the two-dimensional DCT 2020 and quantized 2030. The resultingquantized data is compressed via an entropy removal process 2040,resulting in a compressed data set or stream 2210. A decompressionprocess can then be executed on said compressed data set or stream 2210,comprising the reverse entropy removal step 2110, a de-quantizing step2120, an inverse two-dimensional DCT process 2130, and a block-basedsummation process 2135 using a previously-decompressed reference frame2140 to generate an individual frame ready for playback or otherprocessing 2145. The pre-defined fixed quantizer 2310 utilized in saidquantization process 2030 and said de-quantization process 2130 cannotleverage the Human Vision Model, as no such model has been developed toapply directly to the difference between video blocks.

What is needed is a means of removing subjectively redundant videoinformation from a moving sequence of video.

Many prior-art techniques are taught under the principle of guiding adesign of a quantization matrix to provide optimum visual quality for agiven bitrate. These techniques, being applicable to motioncompensation-based compression algorithms, require a Human VisualModel-driven feedback loop to converge on the quantizers that will showminimal artifact on reconstruction. The use of this Human Visual Modelis again limited to its application in the spatial domain. An example ofthis teaching is U.S. Pat. No. 8,326,067 by Furbeck, as illustrated inFIG. 3. A block-based difference after motion estimation Error!Reference source not found 015 is taken between reference frame(s)Error! Reference source not found 010 and an individual frame to becompressed Error! Reference source not found 005. Said block-baseddifference after motion estimation Error! Reference source not found 015is transformed using the two-dimensional DCT Error! Reference source notfound 020 and quantized Error! Reference source not found 030. Theresulting quantized data is compressed via an entropy removal processError! Reference source not found 040, resulting in a compressed dataset or stream Error! Reference source not found 210. A decompressionprocess can then be executed on said compressed data set or streamError! Reference source not found 210, comprising the reverse entropyremoval step Error! Reference source not found 110, a de-quantizing stepError! Reference source not found 120, an inverse two-dimensional DCTprocess Error! Reference source not found 130, and a block-basedsummation process Error! Reference source not found 135 using apreviously-decompressed reference frame Error! Reference source notfound 140 to generate an individual frame ready for playback or otherprocessing Error! Reference source not found 145. The quantizer Error!Reference source not found 310 utilized in said quantization processError! Reference source not found 030 and said de-quantization processError! Reference source not found 130 cannot directly leverage the HumanVision Model, as no such model has been developed to apply directly tothe difference between video blocks. Therefore a feedback processingstep Error! Reference source not found 240 communicates to a HumanVisual Model Error! Reference source not found 250 which determines theperceptual error, and feeds back recalculated said quantizers Error!Reference source not found 310 to be used to re-compress said individualframe to be compressed Error! Reference source not found 005. Saidfeedback processing step Error! Reference source not found 240 may bebased on simple perceptual error minimization, or may minimizecompression ratio after entropy removal.

The wavelet transform is another technique commonly used to performcompression. However, the wavelet does not decorrelate video, and thusoptimal quantizers based upon a Human Visual Model cannot be calculated.A teaching by Gu et al, U.S. Pat. No. 7,006,568 attempts to address thisissue by segmenting video sequences into similar-characteristic segmentsand calculating 2-D quantizers for each selected segment, chosen toreduce perceptual error in each subband, as illustrated in FIG. 4. Aframe to be compressed Error! Reference source not found 005 isdecomposed into its subbands via wavelet decomposition Error! Referencesource not found 020 and quantized Error! Reference source not found030. The resulting quantized data is compressed via an entropy removalprocess Error! Reference source not found 040, resulting in a compresseddata set or stream Error! Reference source not found 210. Adecompression process can then be executed on said compressed data setor stream Error! Reference source not found 210, comprising the reverseentropy removal step Error! Reference source not found 110, ade-quantizing step Error! Reference source not found 120, a subbandreconstruction process Error! Reference source not found 130 to generatean individual frame ready for playback or other processing Error!Reference source not found 140. The quantizer Error! Reference sourcenot found 330 utilized in said quantization process Error! Referencesource not found 030 and said de-quantization process Error! Referencesource not found 130 cannot directly leverage the Human Vision Model, asno such model has been developed to apply directly to thepoorly-decorrelated video basis of the wavelet decomposition. Thisprior-art teaching subdivides the video stream into regions ofrelatively stable visual performance bounded by scene changes, ascalculated by a scene analysis process Error! Reference source not found310 acting upon said frame to be compressed Error! Reference source notfound 005 and its previous frame in the motion video sequence Error!Reference source not found 010. A visually-weighted analysis processError! Reference source not found 320 then calculates said quantizersError! Reference source not found 330.

The current invention improves the compression process by directlycalculating the visually optimal quantizers for 3-D transform vectors byevaluating the basis behavior of the decorrelated transform space undera time-varying Human Visual Model, as represented by a ContrastSensitivity Function.

SUMMARY OF INVENTION

In accordance with one aspect of the invention, a method is provided forremoval of all subjectively redundant visual information by means ofcalculating optimal visually-weighed quantizers corresponding to thedecorrelating-transformed block decomposition of a sequence of videoimages. The contrast sensitivity of the human eye to the actualtime-varying transform-domain frequency of each transform component iscalculated, and the resolution of the transformed data is reduced by thecalculated sensitivity.

A second aspect of the invention applies specifically to use of the DCTas the decorrelating transform.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a prior-art compressor featuring an optimal spatialtransform and optimal fixed visual quantizers (JPEG).

FIG. 2 depicts a prior-art compressor featuring a sub-optimaltime-varying transform using sub-optimal quantizers fixed or in-bandquantizers (MPEG).

FIG. 3 depicts a prior-art compressor featuring a sub-optimaltime-varying transform and a recursive feedback quantizer calculation togenerate in-band quantizers.

FIG. 4 depicts a prior-art compressor featuring a sub-optimaltime-varying transform using sub-optimal quantizers fixed or in-bandquantizers (wavelet).

FIG. 5 depicts a compression system featuring an optimal time-varyingtransform using configuration parameters to independently generatevisually optimal quantizers in compressor and decompressor.

FIG. 6 describes a typical set of configuration parameters that may beused to generate visually optimal time-varying quantizers.

FIG. 7 defines a typical time-varying contrast sensitivity function.

FIG. 8 defines a visually optimal quantizer in terms of visualresolution and the contrast sensitivity function specified in FIG. 7.

FIG. 9 refines the visually optimal quantizer definition of FIG. 8 withangular data specifications.

FIG. 10 refines the visually optimal quantizer definition of FIG. 8 withoff-axis visual sensitivity human visual system adjustments.

FIG. 11 depicts a typical symmetric contrast sensitivity function(without angular or off-axis corrections).

FIG. 12 depicts typical contrast sensitivity function off-axis visualsensitivity human visual system adjustments.

FIG. 13 depicts typical eccentric-angle visual sensitivity human visualsystem adjustments.

FIG. 14 depicts the location of DC, mixed DC/AC, and AC componentswithin a 3-dimensional DCT block.

FIG. 15 illustrates the calculation of DC component quantizers, and thecontributed DC and AC quantizers of a mixed DC/AC component.

FIG. 16 illustrates the calculation of a statistically ideal mixed DC/ACquantizer.

FIG. 17 illustrates the application of a configurable Gibbs ringingcompensation factor.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

As illustrated in FIG. 5, a block comprising a plurality of individualframes of digitized video Error! Reference source not found 010 istransformed via a three-dimensional DCT Error! Reference source notfound 020 and then quantized Error! Reference source not found 030 toremove imperceptible visual data. An entropy removal process Error!Reference source not found 040 actually compresses the information. Thedecompression process follows an equivalent set of steps in reverse,when a data set or data stream containing the compressed data Error!Reference source not found 210 is decompressed Error! Reference sourcenot found 110 by reversing said entropy removal process, followed by ade-quantization step Error! Reference source not found 120, an inverseDCT step Error! Reference source not found 130, and a resulting block offrames Error! Reference source not found 140 may be displayed orotherwise processed. Said quantizer process Error! Reference source notfound 030 and said de-quantizer process Error! Reference source notfound 120 use quantizers Error! Reference source not found 420 generatedby a quantizer generation process Error! Reference source not found 410.Said quantizer generation process Error! Reference source not found 410calculates said quantizers Error! Reference source not found 420 as afunction of four sets of configuration data, the conditions under whichviewing is expected to take place, and under which visual reconstructionwill have no perceptual error Error! Reference source not found 310, theconfiguration of the video stream Error! Reference source not found 320,the quantizer generation algorithm to be used Error! Reference sourcenot found 330, and the configuration of the applied decorrelatingtransform Error! Reference source not found 340.

In the current embodiment, said configuration of video stream Error!Reference source not found 320 is elaborated in FIG. 6. Saidconfiguration of video stream Error! Reference source not found 010 iscomprised of individual configuration items H Error! Reference sourcenot found 020, the number of pixels per line within the frame, V Error!Reference source not found 030, the number of lines within the frame, RError! Reference source not found 040, the frame rate in frames persecond, B Error! Reference source not found 050, the number of bits usedto represent the luminance value per pixel, and Aspect Error! Referencesource not found 060, the physical aspect ratio or ratio of physicalframe width to physical frame height.

In the current embodiment, said configuration of viewing conditionsError! Reference source not found 310 is elaborated in FIG. 6. Saidconfiguration of viewing conditions Error! Reference source not found110 is comprised of individual configuration items D Error! Referencesource not found 120, the expected viewing distance in screen heights,and I Error! Reference source not found 130, the expected averageambient luminance.

In the current embodiment, said configuration of block-baseddecorrelating transform Error! Reference source not found 340 iselaborated in FIG. 6. Said configuration of block-based decorrelatingtransform Error! Reference source not found 210 is comprised ofindividual configuration items N Error! Reference source not found 220,the number of pixels per transform block, M Error! Reference source notfound 230, the number of lines per transform block, L Error! Referencesource not found 240, the number of frames per transform block,N_(index) Error! Reference source not found 250, the number of framesper transform block, and M_(index) Error! Reference source not found260, the number of frames per transform block.

In the current embodiment, said configuration of quantizer algorithmError! Reference source not found 330 is elaborated in FIG. 6. Saidconfiguration of quantizer algorithm Error! Reference source not found310 is comprised of individual configuration items visual loss factor,Error! Reference source not found 320 Mx, mixed DC/AC coefficientalgorithm, Error! Reference source not found 330 R_(x), R_(y) and R_(z),correlation in pixel, line and frame directions respectively, and Error!Reference source not found 340 dBG, Gibbs ringing compensation.

FIG. 7 defines a typical contrast sensitivity function Error! Referencesource not found 010 CSF(u,w,I,X₀,X_(max)) in terms of said (Error!Reference source not found 130) viewing conditions configuration itemexpected average ambient luminance I Error! Reference source not found040, and additional variables u Error! Reference source not found 020,2-dimensional spatial frequency, w Error! Reference source not found030, temporal frequency, X₀ Error! Reference source not found 050, anglesubtended by DCT block, and X_(max) Error! Reference source not found060, angle subtended by display surface.

Luminance quantizers are calculated as in FIG. 8( a). The equationError! Reference source not found 010 calculates the quantizer Q Error!Reference source not found 020 for a particular decorrelating transformcomponent of index n Error! Reference source not found 030 in the pixeldirection, a particular decorrelating transform component of index mError! Reference source not found 040 in the line direction and aparticular decorrelating transform component of index I Error! Referencesource not found 050 in the frame or time direction, a particulardecorrelating transform component of position M_(index) Error! Referencesource not found 060 in the pixel direction and a particulardecorrelating transform component of position N_(index) Error! Referencesource not found 070 in the line direction; given said two-dimensionalspatial frequency u (Error! Reference source not found 020), saidtemporal frequency w (Error! Reference source not found 030), of said(Error! Reference source not found 130) viewing conditions configurationitem expected average ambient luminance I (Error! Reference source notfound 040), said , angle subtended by DCT block, X₀ (Error! Referencesource not found 050), and said angle subtended by display surfaceX_(max) (Error! Reference source not found 060).

The equation Error! Reference source not found 110 of FIG. 8( b)calculates said temporal frequency of a transform component w (Error!Reference source not found 030) as a function of said configuration ofvideo stream configuration item frame rate in frames per second R(Error! Reference source not found 040), said configuration ofblock-based decorrelating transform configuration item number of framesper transform block L (Error! Reference source not found 240), and saidparticular decorrelating transform component of index in the frame ortime direction I (Error! Reference source not found 050).

The equation Error! Reference source not found 010 of FIG. 9( a) depictsa typical definition of said angle subtended by display surface X_(max)(Error! Reference source not found 060) in terms of said configurationof viewing conditions individual configuration item D the expectedviewing distance in screen heights (Error! Reference source not found120). The equation Error! Reference source not found 020 of FIG. 9( b)depicts a typical definition of said angle subtended by DCT block X₀(Error! Reference source not found 050) in terms of said configurationof block-based decorrelating transform individual configuration item thenumber of pixels per transform block N (Error! Reference source notfound 220) and said configuration of block-based decorrelating transformindividual configuration item the number of lines per transform block M(Error! Reference source not found 230).

Equation Error! Reference source not found 010 of FIG. 10 depicts apreferred process calculating said two-dimensional spatial frequency u(Error! Reference source not found 020) given said particulardecorrelating transform component of index in the pixel direction n(Error! Reference source not found 030), said particular decorrelatingtransform component of index in the line direction m (Error! Referencesource not found 040), said particular decorrelating transform componentof position in the pixel direction M_(index) (Error! Reference sourcenot found 060) and a particular decorrelating transform component ofposition in the line direction N_(index) (Error! Reference source notfound 070). A human visual system orientation response adjustment is reError! Reference source not found 020. A human visual system ex-fovealeccentricity response adjustment is re Error! Reference source not found030.

The two-dimensional map of values assumes by said typical contrastsensitivity function CSF(u,w,I,X₀,X_(max)) (Error! Reference source notfound 010) for equally-weighted is depicted in FIG. 11. The contour mapof FIG. 12( a) further illustrates the symmetric distribution of saidtypical contrast sensitivity function CSF(u,w,I,X₀,X_(max)) (Error!Reference source not found 010), while The contour map of FIG. 12( b)illustrates the application of said human visual system orientationresponse adjustment re (Error! Reference source not found 020) to bettermodel human visual orientation response. The contour map of FIG. 13illustrates the application of said human visual system ex-fovealeccentricity response adjustment r_(e) (Error! Reference source notfound 030) to better model human visual off-axis response.

As illustrated in FIG. 14, said block Error! Reference source not found010 transformed via a three-dimensional DCT (Error! Reference source notfound 020) is comprised a plurality of transform components. Transformcomponent (n=0,m=0,I=0) Error! Reference source not found 020 isclassified as pure DC. Transform components with (n=0) Error! Referencesource not found 030, with (m=0) Error! Reference source not found 040,or with (I=0) Error! Reference source not found 050 are classified asmixed AC/DC. Component where no (I,m,n) is 0 are classified as pure ACcomponents.

Said quantizer Q (Error! Reference source not found 020) gives optimalresponse for pure AC transform components, but produces sub-optimalresults for pure DC or mixed AC/DC components, due to the extremesensitivity of the human eye to DC levels. Pure DC transform componentsmay be quantized by the value that the variance of the DC component isconcentrated over the number of possible levels that can be representedin the reconstructed image, as the human eye is constrained to thecapabilities of the display. Equation Error! Reference source not found010 of FIG. 15( a) defines the pure DC transform quantizer as a functionof said configuration of block-based decorrelating transform individualconfiguration item the number of pixels per transform block N (Error!Reference source not found 220), said configuration of block-baseddecorrelating transform individual configuration item number of linesper transform block M (Error! Reference source not found 230), and saidconfiguration of block-based decorrelating transform individualconfiguration item number of frames per transform block L (Error!Reference source not found 240).

Mixed AC/DC components can be quantized by the minimum quantization stepsize apportioned over the variance of the DCT basis component. Thisprocess requires calculation of the per-component variance for the ACand DC components (i.e., the variance calculation in the number ofdimensions in which each AC or DC component resides). Similarly, thevalue of the independent AC and DC quantizers must be calculated usingthe Contrast Sensitivity Function limited to the number of dimensions inwhich the AC or DC component resides. As illustrated in FIG. 15( b), thepseudocode C language program calcQ Error! Reference source not found110 defines a quantizer suitable for application to the DC portion ofmixed AC/DC components quantizer as a function of said configuration ofblock-based decorrelating transform individual configuration item thenumber of pixels per transform block N (Error! Reference source notfound 220), said configuration of block-based decorrelating transformindividual configuration item number of lines per transform block M(Error! Reference source not found 230), and said configuration ofblock-based decorrelating transform individual configuration item numberof frames per transform block L (Error! Reference source not found 240).Said typical AC/DC component with I=0 Error! Reference source not found050, the one-dimensional DC quantizer Q_(DCm,n,0) Error! Referencesource not found 210 is calculated from said reduced-dimensioncalculation of the quantizer calcQ Error! Reference source not found110.

The two-dimensional AC quantizer Q_(ACm,n,0) Error! Reference source notfound 220 is calculated directly from said typical generalized ContractSensitivity Function CSF(u,w,I,X₀,X_(max)) Error! Reference source notfound 010.

FIG. 16 illustrates the process of deriving a statistically optimalquantizer Q_(m,n,0) Error! Reference source not found 310 from said theone-dimensional DC quantizer Q_(DCm,n,0) Error! Reference source notfound 210 and said two-dimensional AC quantizer Q_(ACm,n,0) Error!Reference source not found 220. Said correlation coefficient Error!Reference source not found 330 Rx is used to generate an autocorrelationmatrix M_(x) Error! Reference source not found 010. The convolution ofsaid autocorrelation with the DCT in the x direction returns thevariance-concentration matrix Cx Error! Reference source not found 020.Said process is understood to apply equally in the y and z directions.

The maximum visual delta of 1/Q_(ACm,n,0) Error! Reference source notfound 110 calculated to apply to the variance-concentrated rangeC_(x)[m,m]*C_(y)[n,n] Error! Reference source not found 120 and1/Q_(DCm,n,0) Error! Reference source not found 130 calculated to applyto the variance-concentrated range Cz[0,0] Error! Reference source notfound 130 is calculated as 1/min(Q_(ACm,n,0) Q_(DCm,n,0)) Error!

Reference source not found 210, and can be applied over the entire rangeC_(x)[m,m]*C_(y)[n,n]* C_(z)[0,0] Error! Reference source not found 220.

Said statistically optimal quantizer Q_(m,n,0) Error! Reference sourcenot found 310 may now be calculated following with the C languagepseudocode excerpt Error! Reference source not found 320. It is to beunderstood that the process of calculating typical statistically idealmixed AC/DC coefficients is illustrated in the general sense in FIG. 15and FIG. 16, with minor changes to the procedure obvious to anyexperienced practitioner of the art.

The worst-case degradation in visual quality caused by the Gibbsphenomenon as a result of quantization is illustrated in FIG. 17 a. Afurther adjustment to visual quality is supported by said Gibbs ringingadjustment Error! Reference source not found 340 dBG, which isinterpreted (FIG. 17 b) as illustrated in equation Error! Referencesource not found 010 as a logarithmic factor of the actual reductionfactor G Error! Reference source not found 020. Said dBG Error!Reference source not found 340 with a value of 0 represents saidquantizer reduction factor G Error! Reference source not found 020 of8.985%, which precisely removes the worst-case Gibbs ringing from havingvisible effect. Gibbs ringing removal is applied to said quantizersError! Reference source not found 420 generated by said quantizergeneration process Error! Reference source not found 410 as illustratedin equation Error! Reference source not found 110 by reduction inmagnitude by the factor 1−G (one minus said factor G Error! Referencesource not found 020).

Thus the present invention presents a comprehensive means ofdetermining, for any given video-decorrelating spatiotemporal transform,optimal visual quantizers under specified viewing conditions and digitalvideo configuration. The rationale behind the development of theseoptimal visual quantizers includes the mapping of a standard contrastspatiotemporal sensitivity model to the specific and potentiallydynamically changing characteristics of the compression system, and theextension of the model to include human sensitivity to angular andoff-axis conditions, and the removal of potential Gibbs artifactsgenerated as a result of quantization. The invention has the importantside-effect of supporting independent coherent quantizer generation incompressor and decompressor, enabling the low data rates associated withfixed quantizer tables while providing adaptation to potentiallychanging video frame rates.

While the present invention has been described in its preferred versionor embodiment with some degree of particularity, it is understood thatthis description is intended as an example only, and that numerouschanges in the composition or arrangements of apparatus elements andprocess steps may be made within the scope and spirit of the invention.

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1. An apparatus comprised of a compressor and decompressor and a methodfor generating an optimally compressed representation ofmultidimensional visual data after transformation by a multidimensionalorthogonal transform of a specified transformation block size, afterquantization by coefficients of said transformation block size, andafter rearrangement of said quantized coefficients into a transmissionsequence, and after collection of said quantized transformationcoefficients into symbols, by the application of said quantizeddecorrelating transform to a plurality of measured variances ofuncompressed multidimensional visual data and measured correlationcoefficients of uncompressed multidimensional visual data to calculatethe probability distribution of each quantized transform coefficientrequired to perform entropy removal,
 2. The method of claim 1 where saidorthogonal transform is the discrete cosine transform,
 3. The method ofclaim 1 where said multidimensional visual data comprises atwo-dimensional still image,
 4. The method of claim 3 where saidtransformation block size comprises the entire image,
 5. The method ofclaim 3 where said plurality of measured variances of uncompressedmultidimensional visual data is one averaged value per block and saidplurality of correlation coefficients is one averaged value per frame,6. The method of claim 3 where said plurality of measured variances ofuncompressed multidimensional visual data is one averaged value perblock and said plurality of correlation coefficients is one averagedvalue per block,
 7. The method of claim 3 where said plurality ofmeasured variances of uncompressed multidimensional visual data is oneaveraged value per dimension per frame and said plurality of correlationcoefficients is one averaged value per dimension per frame,
 8. Themethod of claim 3 where said plurality of measured variances ofuncompressed multidimensional visual data is one averaged value perblock and said plurality of correlation coefficients is one averagedvalue per dimension per block,
 9. The method of claim 1 where saidmultidimensional visual data comprises a three-dimensional moving videosequence,
 10. The method of claim 9 where said transformation block sizecomprises a number of frames by the entire size of a single frame, 11.The method of claim 9 where said plurality of measured variances ofuncompressed multidimensional visual data is one averaged value pergroup of frames and said plurality of correlation coefficients is oneaveraged value per group of frames,
 12. The method of claim 9 where saidplurality of measured variances of uncompressed multidimensional visualdata is one averaged value per block and said plurality of correlationcoefficients is one averaged value per block,
 13. The method of claim 9where said plurality of measured variances of uncompressedmultidimensional visual data is one averaged value per dimension pergroup of frames and said plurality of correlation coefficients is oneaveraged value per dimension per group of frames,
 14. The method ofclaim 9 where said plurality of measured variances of uncompressedmultidimensional visual data is one averaged value per dimension perblock and said plurality of correlation coefficients is one averagedvalue per dimension per block,
 15. The method of claim 1 where saidquantizers are all ones,
 16. The method of claim 1 where said quantizersare all equal,
 17. The method of claim 1 where said quantizers arevisually weighed,
 18. The method of claim 1 where coefficients areorganized within each block into order of decreasing calculatedcomponent variance,
 19. The method of claim 18 where the probability ofsymbols is calculated from a definition of a plurality of symbols ascollected from sequences of component values whose conditionalexpectation is zero followed by the actual non-zero value, a pluralityof symbols as collected from sequences of component values whoseconditional expectation is zero followed by the number of bits requiredto represent the non-zero value, an end-of-block symbol whoseconditional expectation is calculated from the cumulative probability ofa sequence of symbols comprised solely of zeroes, and an escape symbolwhose conditional expectation is calculated from the accumulation of theprobability of all symbols not otherwise defined.
 20. The method ofclaim 1 where coefficients are organized across blocks into order ofdecreasing calculated component variance,
 21. The method of claim 20where the probability of symbols is calculated from a definition of aplurality of symbols as collected from sequences of component valueswhose conditional expectation is zero followed by the actual non-zerovalue, a plurality of symbols as collected from sequences of componentvalues whose conditional expectation is zero followed by the number ofbits required to represent the non-zero value, an end-of-block symbolwhose conditional expectation is calculated from the cumulativeprobability of a sequence of symbols comprised solely of zeroes, and anescape symbol whose conditional expectation is calculated from theaccumulation of the probability of all symbols not otherwise defined.22. The method of claim 1 where coefficients are organized across blocksinto bands of decreasing calculated component variance within of ordersuccessive refinement,
 23. The method of claim 22 where the probabilityof symbols is calculated from a definition of a plurality of symbols ascollected from sequences of component values whose conditionalexpectation is zero followed by the actual non-zero value, a pluralityof symbols as collected from sequences of component values whoseconditional expectation is zero followed by the number of bits requiredto represent the non-zero value, an end-of-block symbol whoseconditional expectation is calculated from the cumulative probability ofa sequence of symbols comprised solely of zeroes, and an escape symbolwhose conditional expectation is calculated from the accumulation of theprobability of all symbols not otherwise defined.
 24. The method ofclaim 1 where coefficients are organized across blocks into bands ofequal weight in order of decreasing calculated component variance, 25.The method of claim 24 where the probability of symbols is calculatedfrom a definition of a plurality of symbols as collected from sequencesof component values whose conditional expectation is zero followed bythe actual non-zero value, a plurality of symbols as collected fromsequences of component values whose conditional expectation is zerofollowed by the number of bits required to represent the non-zero value,an end-of-block symbol whose conditional expectation is calculated fromthe cumulative probability of a sequence of symbols comprised solely ofzeroes, and an escape symbol whose conditional expectation is calculatedfrom the accumulation of the probability of all symbols not otherwisedefined.
 26. The method of claim 1 where Huffman coding based used toperform entropy removal on the constructed stream of symbols,
 27. Themethod of claim 26 where said measured variances of uncompressedmultidimensional visual data and said measured correlations ofuncompressed multidimensional visual data are communicated betweencompressor and decompressor,
 28. The method of claim 1 where arithmeticcoding based is used to perform entropy removal on the constructedstream of symbols,
 29. The method of claim 28 where said measuredvariances of uncompressed multidimensional visual data and said measuredcorrelations of uncompressed multidimensional visual data arecommunicated between compressor and decompressor,
 30. The method ofclaim 1 where said decorrelating transform is any orthonormal wavelet.